In both military and civilian applications, it is often necessary or desirable to be able to determine the location of some target. At sea, for example, a target vessel will often emit radio or other electromagnetic signals. These signals are picked up by direction-finding equipment either on friendly surface vessels or at land-based receiving stations. By analyzing the properties of the signals, one wishes to calculate the position of the broadcasting target vessel.
A similar situation arises in the civilian world, for example, when a vessel in distress broadcasts radio signals which are sensed by land-based receiving stations. Especially in this case, one wishes to be able to determine very quickly where the sending vessel is in order to direct rescue ships or aircraft as accurately as possible.
Perhaps the simplest and most widely known method of locating a signal source is based on the principle of "triangulation." To illustrate this principle, assume that the bearing to a target from each of two receiving stations is known. By drawing the line of bearing (LOB) from each of the receiving stations on a chart, the lines will, in almost all cases, intersect each other in a point. Such an intersection establishes a traditional "fix," and one normally assumes that the target is at or near the fix.
The seeming definiteness of the fix, however, is at best often uncertain and at worst outright dangerous. This is because the reliability of the fix is directly related to the accuracy of the measured variable, in this case, the bearing. In most cases, there will be some measurement error due to the inherent limitations of the measurement equipment and/or as a result of natural disturbances.
The uncertain nature of the fix is usually made apparent as soon as a third line of bearing is taken. Normally, this third LOB will not intersect the other two in the original fix point, but rather will intersect each of the other two lines of bearing at other points. The line segments between each pair of points of intersection form a triangle. Traditionally, one has assumed that the target (or, in the case of celestial, radio, or visual navigation, the position of one's own ship) lies somewhere within the triangle. The certainty of this estimation is typically considered greater the smaller the triangle is.
When a fourth line of bearing is drawn, it will often not intersect the "triangle" at all, and the same applies when additional lines of bearing are drawn. Even though the LOBs do not intersect in a point, each LOB adds information, and the closer the intersections between each pair of LOBs is to the other intersections, the better the "fix" is normally assumed to be.
A problem arises when a line of bearing passes far from all the others. The location or navigation system or operator must then determine whether to assume the deviant LOB is so in error that it is to be excluded, thus losing potentially valuable information. The very fact that the LOBs do not intersect in a point, however, illustrates the uncertainty which arises due to measurement errors. It also illustrates a major drawback of deterministic systems: systems which give a precise determination of latitude and longitude to the operator typically fail to provide the operator with information concerning the probable degree of accuracy of the determination.
U.S. Pat. No. 3,242,494 (Gicca, Mar. 22, 1966) discloses a system for self-location or navigation. The disclosed system is not useful for surveillance purposes. Furthermore, the concept of measurement error is not addressed and the position solution is arrived at in a deterministic manner by solving a set of simultaneous equations. The measurements made in this system are, however, so precise relative to the necessary accuracy that error may be ignored with minimal loss.
U.S. Pat. No. 3,659,085 (Potter, Apr. 25, 1972) discloses an entire system for geolocation. This system uses the conventional method of processing location data and the Potter patent mentions that the well-known weighting technique of "least-squares" is used to reduce errors statistically. One limitation of this system is that it provides only a single mode (probable location area) or answer regardless of how disparate the data is. The system disclosed in the Potter patent is extremely complicated and uses time-of-arrival (TOA) measurements alone, requires a large number of stations, and also requires a "pulsed" type signal. In other words, the Potter patent discloses a specific complete system which is designed to solve a single precise problem using a single type of equipment.
U.S. Pat. No. 3,723,960 (Harris, Mar. 27, 1973) is an acoustic geolocation system which also uses TOA measurements. As in other prior art geolocation systems, the Harris system provides a deterministic solution with no indication of how errors in measurements are resolved.
U.S. Pat. No. 4,031,501 (Caruso, June 21, 1977) similarly describes an acoustic TOA system which neglects errors and which makes the implicit assumption of a single, unambiguous solution which all data must "fit."
U.S. Pat. No. 3,886,553 (Bates, May 27, 1975) describes yet another TOA system, but provides a final solution based on the technique of "pattern recognition," according to which a measured occurrence is compared with a catalogued set of prior occurrences. The Bates system is limited in scope in that it requires TOA measurements and it inferably also requires a high degree of precision since no variance or error models are mentioned. Furthermore, the Bates system provides only a single unique solution.
U.S. Pat. No. 4,275,399 (Marom, June 23, 1981) discloses an antenna system which can be used to determine the direction of arrival of an incoming signal. Although such an antenna arrangement is suitable for incorporation into many geolocation systems, the Marom patent does not address the problem of determining the position of a target.
U.S. Pat. No. 4,621,267 (Wiley, Nov. 4, 1986) describes a system for determining the location of a target based on azimuth and "depression" measurements from aircraft. The Wiley system measures differential times of arrival at various sensors and attempts to determine the position of the target by comparing the differential time measurements to a discrete and predetermined set of possible solutions. The Wiley system is not generally applicable to surface-based location systems.
U.S. Pat. No. 4,799,062 (Sanderford, Jan. 17, 1989) describes yet another TOA scheme, but discloses primarily a hardware configuration. The geolocation method mentioned int he Sanderford patent relies on well-known time-of-arrival calculations. However, the text does not describe its computational scheme, and it is inferable that the Sanderford system is designed to provide a deterministic solution.
U.S. Pat. No. 4,811,308 (Michel, Mar. 7, 1989) describes a system in which acoustic and seismic sensors are combined for use in a tracking system, especially for otherwise undetectable "stealth" aircraft. The ultimate output of this system is a "track," with intermediate point estimates of the location of the target. The method used in this system is nothing more than simple triangulation, taken to be a least-squares or weighted centroid solution.
U.S. Pat. No. 4,860,216 (Linsenmayer, Aug. 22, 1989) describes a system which is primarily concerned with the identification or correlation of signals, and no clear geolocation solution is described in this patent. Furthermore, the Linsenmayer system uses a predetermined set of hypothetical solutions (chafe, fuel tanks, re-entry vehicle, etc.), and attempts to identify the target as one solution in this predetermined set.
Finally, Technical Note 820 of the Naval Ocean Systems Center of San Diego, Calif., entitled "Technical Description of NOSCLOC, an HFDF Fix Program" by D. L. Burdick and M. C. Mudurian, published on Jan. 28, 1980, describes a geolocation system in which the intersections of pairs of LOBs are determined. The intersections are then weighted and the system finally computes a fix, i.e., a single solution, as the weighted centroid of the weighted intersections. An unbiased minimum variance estimate is thereby obtained.
The NOSCLOC system also includes an "outlier routine" which attempts to check the internal consistency of the fixes and, using statistical criteria, excludes measurements which the routine identifies as outliers. Under certain circumstances, the NOSCLOC routine will eliminate all of the measurements from the station whose bearing is the farthest from the median centroid if there are two or more outliers. The disadvantage of this elimination routine is that information is automatically discarded based on a predetermined evaluation routine, even though this information might be of some value to the human operator who must make a decision based on the estimated location of the target.